Degradation, Reliability and Failure Analysis

Introduction

Electrical materials rarely fail because of a single instantaneous event. More commonly, operating temperature, electric field, mechanical stress, moisture, contaminants, radiation, and manufacturing variability interact over time. These influences alter material properties, create defects, and eventually produce loss of required electrical, mechanical, thermal, or safety performance.

Reliability engineering provides methods for predicting this evolution and for deciding whether a component is suitable for service. Failure analysis then identifies the physical mechanism, the initiating cause, and the corrective action. For an electrical engineer, the subject connects materials science with circuit design, power electronics, insulation systems, packaging, manufacturing, maintenance, and safety regulation.

A useful distinction is:

• Degradation is progressive deterioration of a property or function.
• Failure is the inability to meet a specified requirement.
• Fault is an abnormal condition in an operating system.
• Reliability is the probability that an item performs its required function for a stated time, under stated conditions.
• Maintainability is the probability that a failed item can be restored within a stated time and procedure.

A failure statement must therefore specify the criterion. For example, a capacitor may be considered failed when capacitance changes by more than 10%, leakage current exceeds its limit, insulation resistance falls below specification, or the part becomes unsafe.

Learning objectives

By the end of this chapter, a student should be able to:

1. Model thermal, electrical, mechanical, and environmental ageing.
2. Explain electromigration, fatigue, corrosion, insulation breakdown, and thermal-cycling damage.
3. Apply Arrhenius and humidity–temperature–bias models within their limitations.
4. Use accelerated testing without confusing acceleration with proof of field life.
5. Interpret reliability data using exponential and Weibull models.
6. Conduct a structured root-cause and failure-analysis investigation.
7. Select condition-monitoring variables and interpret their trends.
8. Evaluate design, manufacturing, and maintenance actions that improve reliability.

1. Degradation as a coupled materials process

A material property can be represented as a time-dependent state variable, such as resistance, dielectric strength, crack length, insulation resistance, contact force, or thermal conductivity. A general degradation model is

where D is a degradation indicator, D₀ is its initial value, T is temperature, E is electric field, σ is mechanical stress, H represents humidity or chemical exposure, N is the number of cycles, and g is an experimentally determined function. No universal form of g exists; the chosen model must correspond to the physical mechanism and the measured failure criterion.

The main stress classes are:

The engineering task is not merely to find a correlation. It is to establish whether the stress accelerates the same failure mechanism that occurs in service.

2. Thermal ageing and reaction-rate models

Many chemical and diffusion-controlled degradation processes accelerate with temperature. A common empirical model is the Arrhenius relation:

Here k is the degradation rate, A is a pre-exponential constant, Eₐ is activation energy in J mol⁻¹, R = 8.314 J mol⁻¹ K⁻¹, and T is absolute temperature in kelvin. The model assumes one dominant thermally activated mechanism over the temperature range considered.

If failure occurs after a fixed amount of degradation, life L is approximately inversely proportional to k. The acceleration factor for testing at T_test relative to operation at T_use is therefore

Temperatures must be in kelvin. The expression should not be extrapolated through a mechanism change, melting transition, phase change, or a different oxidation regime.

Worked example: thermal acceleration

A polymer insulation process has Eₐ = 0.70 eV. Converting to molar units gives Eₐ ≈ 0.70 × 96 485 = 67 540 J mol⁻¹. Estimate the acceleration from 90 °C testing to 60 °C service.

T_test = 363.15 K and T_use = 333.15 K. Thus,

AF = exp[(67 540/8.314)(1/333.15 − 1/363.15)]

The reciprocal-temperature difference is approximately 0.000248 K⁻¹, and the exponent is approximately 2.02. Therefore AF ≈ exp(2.02) ≈ 7.5. A 1 000 h test corresponds to approximately 7 500 h only if the same mechanism and failure criterion apply.

A temperature index is sometimes used for polymers, but it is a specification-oriented summary, not a replacement for mechanism-based analysis. Thermal ageing may also cause thermal runaway: increased resistance, contact resistance, or dielectric loss produces heat, which raises temperature and further increases degradation.

For a component with generated power P and thermal resistance θ_JA, a simple steady-state estimate is

where T_J is junction temperature, T_A is ambient temperature, and θ_JA is in K W⁻¹. This relation assumes steady state and a reasonably linear thermal path. Transient operation requires a thermal impedance Z_θ(t), not merely θ_JA.

3. Electrical ageing and insulation failure

Electrical ageing mechanisms include dielectric heating, charge injection, partial discharge, electrical treeing, space-charge accumulation, and field-assisted chemical degradation.

For a uniform dielectric of thickness d under voltage V, the average field is

This is only an average field. Electrodes, voids, sharp edges, contamination, and cracks produce local field enhancement. A void in solid insulation can experience a higher local field because its permittivity differs from that of the surrounding material.

Partial discharge and electrical treeing

Partial discharge is a localized electrical breakdown that does not completely bridge the insulation between electrodes. Repeated discharge deposits heat, chemical products, and charge, gradually enlarging defects. Electrical treeing is the branching growth of channels through an insulating polymer under sustained electrical stress. Failure is often preceded by increasing discharge magnitude, pulse repetition, or changes in phase-resolved discharge patterns.

The time-to-breakdown relation is often represented empirically by an inverse-power law:

where t_b is breakdown time, C is a fitted constant, E is electric field, and n is an experimentally determined exponent. This is not a universal law; it applies only over the field and material range for which the data support the model.

Moisture reduces surface insulation resistance, increases ionic conduction, plasticizes some polymers, and can promote electrochemical migration. A bias applied across contaminated conductors may produce dendritic metallic growth and eventual short circuit.

4. Environmental ageing: a quantitative humidity–temperature–bias model

Environmental ageing is governed by moisture transport, chemical reaction, ionic mobility, and electrical stress. A useful engineering model for a humidity-sensitive failure is a Peck-type relationship:

where L is life, RH is relative humidity expressed as a fraction, V is applied voltage or another electrical-stress measure, C is a fitted constant, m and n are empirical humidity and voltage exponents, and Eₐ is an activation energy. The model assumes that the same humidity-assisted, electrically biased mechanism operates in both test and service conditions. It is not valid when condensation, liquid water, corrosion morphology, or a new failure mechanism appears.

For two conditions, the acceleration factor from service condition 1 to test condition 2 is

Worked example: humidity, temperature, and bias

Suppose a conformal-coated circuit has fitted parameters m = 2, n = 1.5, and Eₐ = 0.60 eV = 57 891 J mol⁻¹. Compare service at 25 °C, 60% RH, and 12 V with a test at 55 °C, 85% RH, and 24 V.

Use T₁ = 298.15 K, T₂ = 328.15 K, RH₁ = 0.60, RH₂ = 0.85. The three factors are:

• Humidity factor: (0.85/0.60)² ≈ 2.01.
• Temperature factor: exp[(57 891/8.314)(1/298.15 − 1/328.15)] ≈ exp(2.16) ≈ 8.67.
• Voltage factor: (24/12)^1.5 = 2^1.5 ≈ 2.83.

Therefore AF ≈ 2.01 × 8.67 × 2.83 ≈ 49.3. A 1 000 h test would represent approximately 49 300 h under the model, or about 5.6 years. This result is conditional, not a guarantee: if the test causes condensation while service does not, or if corrosion changes from surface leakage to galvanic attack, the extrapolation is invalid.

Good environmental qualification reports record temperature, RH, condensation state, ionic contamination, bias polarity, voltage, current, coating condition, and failure criterion. “85/85 testing” is a stress condition, not automatically a field-life prediction.

5. Electromigration in conductors

Electromigration is the transport of metal atoms caused by high current density. Momentum transfer from conducting electrons, called the electron-wind force, generally drives atoms in the direction of electron flow. In a conventional metal conductor, electrons move from the negative terminal toward the positive terminal; therefore electron-wind atomic transport is generally from cathode toward anode.

The resulting damage pattern is especially important:

• Voids tend to form near the cathode, where atomic depletion occurs.
• Hillocks, extrusions, and accumulation tend to form near the anode, where atoms accumulate.
• A void raises local resistance and current density, increasing Joule heating and promoting further damage.
• An anode hillock may bridge adjacent conductors and cause a short circuit.

The direction can be modified by temperature gradients, mechanical stress, interfacial diffusion, and material structure, so microscopy and electrical geometry must be considered before assigning polarity.

A commonly used lifetime relation is Black’s equation:

where MTTF is mean time to failure, j is current density, n is an empirical current-density exponent, Eₐ is activation energy, k_B is Boltzmann’s constant, T is absolute temperature, and A is a fitted constant. The equation is empirical and should not be used outside the range of the calibration data.

Design controls include reducing current density, avoiding abrupt conductor-width changes, improving barrier and cap layers, controlling grain structure, limiting temperature, and eliminating process residues. Failure analysis commonly uses cross-sectional microscopy, focused-ion-beam sectioning, energy-dispersive spectroscopy, and resistance history.

6. Mechanical fatigue, creep, and thermal cycling

Mechanical fatigue occurs when repeated stress or strain causes crack initiation and growth. In metals, the stress-life relation is often fitted with a Basquin form:

where σₐ is stress amplitude, σ′_f and b are fitted material constants, and N_f is the number of cycles to crack initiation or defined failure. The equation assumes a specified loading ratio and material condition.

For solder joints and other ductile interconnects, inelastic strain is often more relevant. A Coffin–Manson form is

where Δε_p/2 is plastic-strain amplitude and ε′_f and c are fitted constants. Creep may occur simultaneously, particularly at elevated temperature. Consequently, a simple elastic stress calculation can substantially underpredict damage.

Thermal cycling produces differential expansion. For two bonded materials, a first-order mismatch strain is

where α₁ and α₂ are coefficients of thermal expansion and ΔT is the temperature excursion. If the interface constrains this strain, stress develops. In a fully constrained linear-elastic approximation, σ ≈ E Δε_m, but this relation is not appropriate when the material yields, creeps, delaminates, or has complex geometry.

Thermal-cycle damage is assessed by monitoring crack resistance, electrical continuity, daisy-chain resistance, acoustic emission, microscopy, or X-ray imaging. Cycle rate matters because it changes dwell time, creep, heat transfer, and moisture diffusion. Thus, a rapid laboratory cycle may not reproduce a slow field cycle.

7. Corrosion and electrochemical failure

Corrosion is the chemical or electrochemical degradation of a material. In electronics it may appear as uniform corrosion, pitting, galvanic corrosion, crevice corrosion, fretting corrosion, or electrochemical migration.

A galvanic cell requires an anode, cathode, electrolyte, and an electrically conductive path. At the anode, metal dissolves; at the cathode, a reduction reaction occurs. The corrosion rate is affected by potential difference, area ratio, electrolyte conductivity, pH, temperature, oxygen, and contamination.

Faraday’s law connects charge transfer to mass loss:

where m is dissolved mass, M is molar mass, I is corrosion current, t is time, z is the number of electrons per metal atom, and F ≈ 96 485 C mol⁻¹. This ideal relation assumes that the measured current is associated with the stated corrosion reaction; side reactions reduce its accuracy.

Prevention includes compatible material pairs, protective finishes, sealing, drainage, cleanliness, controlled ionic contamination, and avoidance of stagnant electrolytes. A coating must be evaluated for pinholes, adhesion, water absorption, repairability, and long-term chemical compatibility.

8. Reliability models and accelerated testing

For a constant failure rate λ, the exponential reliability model is

where R(t) is survival probability to time t and λ has units of time⁻¹. The model is appropriate only over a period in which the hazard rate is approximately constant. It is not generally suitable for infant mortality or wear-out.

The Weibull model is more flexible:

where β is the shape parameter and η is the characteristic life, defined by R(η) = exp(−1) ≈ 0.368. The hazard function is

Interpretation is central:

• β < 1: decreasing hazard, often process defects or infant mortality.
• β = 1: constant hazard, equivalent to the exponential model.
• β > 1: increasing hazard, commonly wear-out or accumulated damage.

For uncensored ordered failure times t_i, a rough median-rank estimate is F_i ≈ (i − 0.3)/(N + 0.4), where N is the number of failures. A Weibull plot uses ln[−ln(1 − F)] against ln t. Its slope estimates β. Real qualification data often contain right-censored units, so maximum-likelihood or regression methods designed for censoring should be used rather than simply discarding survivors.

Accelerated testing increases stress to obtain failures in practical time. Valid acceleration requires:

1. The same dominant mechanism in test and service.
2. A known or justified stress–life relationship.
3. Appropriate control of secondary stresses.
4. A failure criterion relevant to function and safety.
5. Adequate sample size and treatment of censored observations.

Overstress tests are useful for robustness screening but may reveal a different mechanism from normal use. HALT can expose design weaknesses through stepwise overstress; it is not, by itself, a statistical life demonstration.

9. Failure-analysis methodology

A disciplined investigation preserves evidence before interpretation. The recommended sequence is:

1. Define the failure. State the function, limit, operating history, and time of failure.
2. Secure evidence. Photograph, label, isolate, and preserve the failed item. Avoid cleaning or powering it unnecessarily.
3. Reconstruct history. Gather manufacturing records, thermal profiles, electrical logs, environmental exposure, repairs, and lot information.
4. Perform non-destructive examination. Use visual inspection, X-ray, infrared imaging, electrical characterization, ultrasonic methods, or microscopy without sectioning.
5. Localize the defect. Compare failed and known-good units.
6. Use destructive analysis carefully. Cross-section, polish, chemically analyze, and inspect interfaces only after evidence is recorded.
7. Form competing hypotheses. Consider design, material, process, assembly, application, and maintenance causes.
8. Verify the cause. Reproduce the failure or eliminate it through a controlled experiment.
9. Implement corrective action. Change design, process, supplier controls, environmental protection, or monitoring.
10. Confirm effectiveness. Retest representative units and verify that no new failure mode has been introduced.

A fault tree begins with a top event and logically combines causes using AND and OR gates. Failure-mode and effects analysis (FMEA) begins with component-level failure modes and evaluates effects, causes, controls, severity, occurrence, and detectability. Risk-priority numbers can support discussion, but they should not replace engineering judgment or severity-based escalation.

Root-cause analysis should distinguish:

• Physical root cause: the mechanism, such as a fatigue crack.
• Technical cause: the stress that produced it, such as excessive strain range.
• Systemic cause: why the design or process allowed the stress, such as inadequate thermal-mechanical verification.

10. Condition monitoring and prognostics

Condition monitoring measures variables that change before functional failure. Examples include winding temperature, partial-discharge activity, insulation resistance, leakage current, contact resistance, vibration, acoustic emission, thermal impedance, and harmonic content.

A useful monitoring system has a baseline, a measurement uncertainty, a sampling plan, and an alarm rule. A trend is usually more informative than a single threshold crossing. For a measured quantity x with baseline mean μ and standard deviation σ, a simple standardized indicator is

This assumes that the baseline distribution is stable and approximately described by μ and σ. It is not automatically valid for drifting, non-Gaussian, or strongly load-dependent data.

Physics-of-failure prognostics estimates remaining useful life from a damage model, such as crack growth or insulation resistance decline. Data-driven machine-learning models can identify patterns in large monitoring datasets, but they require representative labelled data, protection against sensor drift, explainability for safety decisions, and validation on operating conditions not used for training. AI should support—not replace—physical inspection and engineering authorization.

11. Illustrative case study: power-module field failures

Background

A three-phase inverter used in an industrial drive experiences intermittent open-circuit faults after approximately 18 months. The module contains ceramic substrates, solder layers, copper metallization, and bonded semiconductor dies.

Problem

Field returns show high case temperature and electrical intermittency, but no consistent semiconductor overvoltage event. The manufacturer initially suspects random die defects.

Analysis

The investigation compares returned modules with unused controls. X-ray imaging shows no gross voiding difference. Cross-sections reveal cracks in the die-attach solder near the perimeter. The crack path follows regions of high thermomechanical strain. Logged operation shows frequent start–stop cycles and load changes, producing large junction-temperature excursions. A thermal model indicates that copper and ceramic expansion mismatch imposes cyclic shear strain on the solder.

A daisy-chain resistance measurement during accelerated thermal cycling shows gradual resistance increases followed by abrupt open circuits. Weibull analysis gives β > 1, indicating an increasing wear-out hazard rather than random infant mortality. Metallography confirms fatigue and creep damage, not electromigration or corrosion.

Approach and solution

The design team reduces junction-temperature swing by improving cooling and control strategy, increases solder fatigue resistance, modifies die-attach geometry, and validates the change using representative thermal cycles with realistic dwell times. Manufacturing inspection is added for solder void distribution, and field monitoring records thermal-cycle counts.

Outcome

The redesigned module shows no open circuits during the qualification interval, and its measured resistance remains stable. The organization also changes its failure reporting so that temperature history and cycle count accompany every return.

Learning points

The case illustrates that:

• A visible electrical symptom may originate in a mechanical material failure.
• Increasing Weibull β supports a wear-out interpretation.
• Accelerated testing must reproduce the relevant strain and temperature history.
• Corrective action should address the physical, technical, and systemic causes.
• Monitoring a damage driver, such as junction-temperature cycles, may be more useful than monitoring only the final fault.

12. Design and professional practice

Reliability should be designed in rather than tested in at the end. Important practices include derating voltage, current, temperature, and mechanical stress; controlling interfaces and contamination; specifying material compatibility; designing for inspection and repair; and documenting mission profiles.

Safety-critical decisions require traceability, independent review, calibrated instruments, and conservative treatment of uncertainty. Environmental and accelerated tests should follow applicable product and industry standards, but compliance does not eliminate the need for mechanism-based engineering judgment. Failure records may contain customer or operational data and must be handled with appropriate confidentiality and cybersecurity controls.

Contemporary reliability engineering increasingly combines multiphysics simulation, digital mission profiles, embedded sensors, automated microscopy, and statistical learning. These tools are valuable when their assumptions, training data, uncertainty, and failure criteria are explicit. A sophisticated model with poor material data remains unreliable.

Chapter Summary

Electrical-material degradation results from interacting thermal, electrical, mechanical, chemical, and environmental stresses. Arrhenius models describe many thermally activated processes, while humidity–temperature–bias models can quantify environmental acceleration when their mechanism assumptions are satisfied. Electromigration generally transports atoms from cathode to anode under electron-wind action, producing cathode-side voids and anode-side accumulation. Fatigue, creep, thermal-expansion mismatch, corrosion, partial discharge, and electrical treeing are major causes of field failure.

Reliability models translate test observations into survival probabilities. The exponential model applies to approximately constant hazard, whereas the Weibull shape parameter distinguishes decreasing, constant, and increasing hazard. Accelerated testing is defensible only when the same mechanism operates in test and service. Failure analysis requires evidence preservation, non-destructive examination, competing hypotheses, verification, and corrective action. Condition monitoring is most effective when it tracks a physical damage driver and uses validated trends. Good engineering combines materials knowledge, statistical analysis, design control, manufacturing discipline, and ethical management of safety and uncertainty.

Key Terms

Degradation: Progressive deterioration of a material property or function.

Failure: Inability to meet a specified requirement.

Reliability: Probability of performing a required function for a stated time and condition.

Activation energy: Energy parameter governing a thermally activated rate.

Arrhenius model: Temperature–rate relationship based on exponential activation-energy behavior.

Acceleration factor: Ratio of service life to test life under a stated model.

Partial discharge: Localized discharge that does not completely bridge insulation.

Electrical treeing: Branching channel growth through insulation under electrical stress.

Electromigration: Current-induced transport of metal atoms.

Electron wind: Momentum-transfer force exerted by conducting electrons on atoms.

Void: Material-depleted region, often increasing resistance or reducing mechanical area.

Hillock: Local protrusion caused by atomic accumulation.

Fatigue: Damage caused by repeated stress or strain.

Creep: Time-dependent deformation, often significant at elevated temperature.

Corrosion: Chemical or electrochemical material deterioration.

Weibull distribution: Reliability distribution characterized by shape and scale parameters.

Hazard rate: Instantaneous conditional failure rate.

Failure mode: The manner in which a component fails.

Root cause: Underlying cause whose removal prevents recurrence.

Condition monitoring: Measurement of variables that indicate evolving condition.

Review Questions

Short Answer Questions

1. Distinguish degradation, failure, fault, and reliability.
2. State the assumptions required for use of an Arrhenius acceleration factor.
3. Why do electromigration voids commonly develop near the cathode?
4. What do Weibull shape parameters β < 1 and β > 1 indicate?
5. Name four observations that should be recorded before destructive failure analysis.

Long Answer Questions

1. Explain thermal cycling damage in a soldered power module, including expansion mismatch, creep, fatigue, and suitable monitoring methods.
2. Describe partial discharge, electrical treeing, and the influence of voids and field enhancement on insulation failure.
3. Compare exponential and Weibull reliability models and explain when each is appropriate.
4. Explain corrosion and electrochemical migration in a contaminated printed-circuit assembly and propose preventive controls.
5. Develop a failure-analysis workflow from field return to verified corrective action.

Analytical / Application Questions

1. A test is performed at 70 °C and service occurs at 40 °C. Given Eₐ = 0.65 eV, calculate the Arrhenius acceleration factor and state two reasons why the result might be invalid.
2. A biased humidity test uses 90% RH, 50 °C, and 20 V, while service uses 60% RH, 25 °C, and 10 V. Using m = 2, n = 1, and Eₐ = 0.55 eV, calculate the model-based acceleration factor and discuss the effect of condensation.
3. A returned power module has increasing daisy-chain resistance after repeated thermal cycles. Propose a sequence of non-destructive and destructive examinations and explain how Weibull β would influence your diagnosis.

Multiple Choice Questions with Answers

Question 1

Under conventional electron-wind electromigration, which failure-location pattern is generally expected?

A. Voids near the cathode and atomic accumulation near the anode

B. Voids near the anode and atomic accumulation near the cathode

C. Voids equally distributed with no polarity dependence

D. Hillocks only at the cathode and no anode effect

Correct Answer: A. Voids near the cathode and atomic accumulation near the anode

Question 2

In the Arrhenius acceleration factor, temperatures must be expressed in which units?

A. Degrees Celsius

B. Degrees Fahrenheit

C. Kelvin

D. Electron-volts

Correct Answer: C. Kelvin

Question 3

For a Weibull distribution, β greater than 1 generally indicates:

A. A decreasing hazard rate

B. A constant hazard rate

C. An increasing hazard rate

D. Zero probability of failure

Correct Answer: C. An increasing hazard rate

Question 4

A humidity–temperature–bias life model is most defensible when:

A. The test deliberately causes a different failure mechanism

B. The same dominant mechanism operates in test and service

C. Relative humidity is ignored

D. The voltage is always zero

Correct Answer: B. The same dominant mechanism operates in test and service

Question 5

Which observation is most characteristic of thermal-fatigue damage in a power-module solder layer?

A. A crack associated with repeated temperature excursions

B. A permanent increase in dielectric permittivity only

C. A cathode-side electromigration void in a thin metal line

D. A random software reset without material damage

Correct Answer: A. A crack associated with repeated temperature excursions

Question 6

In the relation m = (MIt)/(zF), z represents:

A. Absolute temperature

B. Number of electrons transferred per atom

C. Electrical resistivity

D. Relative humidity

Correct Answer: B. Number of electrons transferred per atom

Question 7

What is the principal limitation of using a simple steady-state relation T_J = T_A + Pθ_JA during rapidly changing loads?

A. It requires temperature in Celsius only

B. It ignores transient thermal impedance and thermal history

C. It cannot be used for any electrical device

D. It predicts corrosion instead of temperature

Correct Answer: B. It ignores transient thermal impedance and thermal history

Question 8

A Weibull shape parameter β less than 1 is commonly associated with:

A. Infant mortality or early defects

B. Pure wear-out

C. Constant hazard only

D. Guaranteed survival

Correct Answer: A. Infant mortality or early defects

Question 9

Which action should normally occur before sectioning a failed electronic component?

A. Discarding the operating history

B. Cleaning the component aggressively

C. Recording and preserving its original condition

D. Applying maximum voltage to reproduce failure immediately

Correct Answer: C. Recording and preserving its original condition

Question 10

Why can an accelerated test produce an invalid field-life prediction?

A. The test uses a clock

B. The accelerated stress may activate a different failure mechanism

C. All accelerated tests are statistically impossible

D. Failure criteria never matter

Correct Answer: B. The accelerated stress may activate a different failure mechanism